Right from the start, you need to clarify with all the major players -- your fiance, parents and officiants -- what the expectations are and what everyone wants. You and your officiant(s) should also figure out how the ceremony will be orchestrated and organized. Establishing the basic parameters for your wedding ceremony will make planning it that much simpler.
Vows
There are several ways you can go. You could pick vows from one faith or combine words from both traditions. Another option is to write your own: If you want to go truly interfaith, writing your own wedding words ensures that neither faith is predominating.
Readings
Your readings are another way you can honor different backgrounds. In addition to the actual words, who you ask to say them can also be a symbolic gesture. You might want to have a member of each of your families read a selection from their own religion -- or you could even mix it up and have them each read something from the other's faith.
Keep Communication Open
If you decide to have more than one officiant, be clear with both about what you want. Busy schedules may prevent a meeting before the wedding, and you'll likely be the main contact. Remember to share discussions with both officiants to prevent misunderstandings.